Thermal dispersion mass flow meters directly measure the mass flow rate of single-phase pure gases and gas mixtures of known composition flowing through pipes or other flow conduits. They also have application to single-phase liquids of known composition. In most of the following, it is assumed that the fluid is a gas, without the loss of applicability to liquids.
The mass flow rate of a fluid (defined by its average velocity multiplied by its mass density multiplied by the cross-sectional area of the channel through which the flow travels) is a measured quantity of interest in the control or monitoring of most practical and industrial applications, such as any chemical reaction, combustion, heating, cooling, drying, mixing, fluid power, etc. For such purposes, gases monitored by industrial thermal dispersion mass flow meters typically include: air, methane, natural gas, carbon dioxide, nitrogen, oxygen, argon, helium, hydrogen, propane, and stack gases, as well as mixtures of these gases and mixtures of hydrocarbon gases.
Generally speaking, a thermal anemometer (alternatively referred to as a thermal dispersion mass flow meter or simply as a mass flow meter) is used to measure the mass velocity at a point or small area in a flowing fluid—be it liquid or gas. The mass velocity of a flowing fluid is its velocity referenced to standard (or normal) temperature and pressure. The mass velocity averaged over the flow channel's cross-sectional area multiplied by the cross-sectional area is the standard (or normal) volumetric flow rate through the channel and is a common way of expressing the total mass flow rate through the channel.
The thermal anemometer is sometimes referred to as an immersible thermal mass flow meter because it can be immersed in a flow stream or channel in contrast to other thermal mass flow meter systems, such as those that sense the total mass flow rate by means of a heated capillary tube mounted externally to the flow channel.
The first general description of a thermal anemometer is attributed to L. V. King who, in 1914, published “King's Law” revealing how a heated wire immersed in a fluid flow measures the mass velocity at a point in the flow: King, L. V. 1914, “On the convection of heat from small cylinders in a stream of fluid: Determination of the convection constants of small platinum wires with application to hot-wire anemometry.” Phil. Trans. Roy. Soc. A214: 373-432. King called his instrument a “hot-wire anemometer.”
Early applications of this technology were hot-wire and hot-film anemometers and other light-duty thermal dispersion flow sensors used in fluid mechanics research and as light-duty mass flow meters and point velocity instruments. It was not until the 1960s and 1970s that industrial-grade thermal dispersion mass flow meters emerged that could solve the wide range of general industry's more ruggedized needs for directly measuring the mass flow rate of air, natural gas, and other gases in pipes and ducts.
Thermal dispersion mass flow meters measure the heat convected into the boundary layer of a fluid (e.g., liquid or gas) flowing over the surface of a heated velocity sensor immersed in the flow. Since it is the molecules of the gas that bear its mass and carry away the heat, thermal dispersion mass flow meters directly measure mass flow rate. In a constant-temperature mode of operation, the “heated” sensor (as commonly known) incorporated in the design is maintained at an average constant temperature above the fluid temperature. The temperature difference between the flowing fluid and the heated sensor results in an electrical power demand in maintaining this constant temperature difference that increases in proportion to the fluid mass flow rate that can be calculated. In another approach, some thermal anemometers operate in a constant-current mode in which a constant current or power is applied to the heated sensor and the fluid mass flow rate is calculated from the difference in the temperature of the heated sensor and the fluid temperature sensor, which decreases as mass flow rate increases.
Thermal anemometers may have greater application to gases, rather than liquids, because their sensitivity in gases is higher than in liquids. However certain examples described herein may be equally applicable to mass flow meters for use with liquids.
Many of the mass flow meters currently known may have shortcomings, some or all of which may be addressed by the present disclosure. For example, because the parts of the heated sensor of known thermal anemometers are not sufficiently reproducible (i.e., dimensionally or electrically), known thermal anemometers require multi-point flow calibration of electrical output versus mass flow rate, in the actual fluid with which they will be used and within the actual ranges of fluid temperature and pressure of the particular application. With such a multi-point flow calibration, some level of flow measurement accuracy may be attainable, however the accuracy is only be applicable to the particular fluid used for calibration only within the narrow ranges of fluid temperature and pressure within which the calibration was conducted.
For industrial applications, the separate heated velocity and fluid temperature sensors are typically enclosed in a protective housing shell. Sometimes, the heated sensor is inserted into the tip of the housing shell and surrounded by a potting compound, such as epoxy, ceramic cement, thermal grease, or alumina powder. In such systems, “skin resistance” and stem conduction are two major contributors to non-ideal behavior and measurement errors. The so-called “skin resistance” is the electrical analog of thermal resistance occurring between the encased heated sensor and the external surface of the housing exposed to the fluid flow. Hot-wire thermal anemometers have zero skin resistance, but thermal anemometers with a housing shell do have some skin resistance. The use of a potting compound substantially increases the skin resistance because such potting compounds have a relatively low thermal conductivity and are relatively thick.
Skin resistance (in units of degrees Kelvin per watt) results in a temperature drop between the encased heated sensor and the external surface of the housing that increases as the electrical power supplied to the heated sensor increases. Skin resistance creates a “droop” and decreased sensitivity in the power versus fluid mass flow rate calibration curve, especially at higher mass flow rates. The so-called droop is difficult to quantify and usually varies from meter to meter because of variations in manufacturing repeatability and in installation. The ultimate result of these skin-resistance problems is reduced accuracy. Furthermore, the use of a surrounding potting compound can create long-term measurement errors caused by aging and by cracking due to differential thermal expansion between the parts of the heated sensor.
Accordingly, the highest quality heated sensors have a skin resistance with a low numerical value that remains constant over the long term. Of all known sensor configurations, the most successful at managing these tradeoffs has been produced by the assignee hereof, Sierra Instruments in U.S. Pat. Nos. 5,880,365; 6,971,274; 7,197,953 and/or 7,748,267, the disclosures of which patents are incorporated herein by reference in their entirety.
Velocity sensor probes constructed as such may be known as “dry” sensors in contrast to velocity sensors fabricated with potting cements or epoxies that are wet when mixed. As discussed, these “wet” velocity-sensor systems suffer long-term stability and other quality issues due to changes in the potting compound. With regards to the temperature sensors, degradation of any potting material incorporated in temperature sensor probes may only change response time, which may be a relatively minor effect, and as such temperature sensor probes may employ any convenient construction.
A significant source of potential error in either the temperature sensor probe and/or velocity sensor probe relates to heat conduction along the probe stem. For example, stem conduction causes a large fraction of the electrical power supplied to the heated sensor to be lost through the stem of the heated sensor, down the housing, lead wires, and other internal parts of the heated sensor and ultimately to the exterior of the fluid flow channel. Stem conduction couples the electrical power supplied to the encased heated sensor to the ambient temperature outside the channel. Typically, if the ambient temperature decreases, stem conduction increases; if ambient temperature increases, the conduction decreases. In either case, as ambient temperature changes, stem conduction changes, and measurement errors occur. Similarly, stem conduction is responsible for errors in the encased fluid temperature sensor's measurement because the fluid temperature sensor also is coupled to the ambient temperature in this manner. Mass flow meters known in the art do not account for stem conduction in sufficient manner to achieve the measurement accuracy as may be desired in certain applications.
Accordingly, the examples described herein may provide systems and methods for measuring mass flow of a fluid with improved performance, including (but not limited to) the ability to meter different fluids without requiring flow calibration specific to the fluid or conditions being monitored, as well as the ability to account for mode(s) of stem conduction heretofore unrecognized and, thus, obtain measurements with increased accuracy.